Meaningfulness and order-invariance: Two fundamental principles for scientific laws

摘要

The first invariance principle, called "meaningfulness," is germane to the common practice requiring that the form of a scientific law must not be altered by a change of the units of the measurement scales. By itself, meaningfulness does not put any constraint on the possible data. The second principle requires that the output variable is "order-invariant" with respect to any transformation ( of one of the input variables) belonging to a particular family or class of such transformations which are characteristic of the law. These principles are formulated as axioms of a theory. Taken together, meaningfulness and order-invariance axioms have strong consequences on the feasible theories. Three applications of our results are discussed in details, involving the Lorentz-FitzGerald contraction, Beer's law, and the Monomial laws, each of which is derived from three axioms implementing meaningfulness and order-invariance concepts. (An "initial condition" axiom is also used.) Not all scientific laws are order-invariant in the sense of this paper. An example is van der Waals' equation.